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An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients. (English) Zbl 0864.35031

The authors construct an example of an “irregular” solution (not \(C^1\)) to the nonlinear Euler-Lagrange elliptic system with real analytic coefficients for very low Euclidean dimensions \((n\geq 5)\). The result improves the one given in [J. Nečas, Theor. Nonlin. Oper., Constr. Aspects, Proc. Int. Summer Sch., Berlin 1975, 197-206 (1977; Zbl 0372.35031)] for very high Euclidean dimensions. The case \(n=4\) is still an open problem.

MSC:

35J35 Variational methods for higher-order elliptic equations
35J60 Nonlinear elliptic equations

Citations:

Zbl 0372.35031
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References:

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